Class 10 Maths Chapter 11 Areas Related to Circles MCQs Quiz

Are you confused by the formulas and concepts in Chapter 11, ‘Areas Related to Circles’? Are problems involving the area of a sector or segment causing you trouble? Don’t worry! We have the perfect solution for you: the Class 10 Maths Chapter 11 Areas Related to Circles MCQs Quiz. This free online test will help you practice all the important formulas and concepts of this chapter. Let’s make your board exam preparation stronger with this helpful Areas Related to Circles quiz!

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Areas Related to Circles MCQs Quiz

Click the Start button to begin the quiz and attempt all questions within the given time. Read each MCQ carefully, select the correct option, and move forward to complete the quiz. Your score will appear at the end to help you check your preparation level..

Q1: What is the part of a circle that is bounded by two radii and the arc between them called?

A: Sector
B: Segment
C: Arc
D: Radius

Explanation: The region bounded by two radii and the arc between them is called a sector.

Q2: What is the part of a circle that is bounded by an arc and the chord joining the ends of the arc called?

A: Sector
B: Segment
C: Arc
D: Radius

Explanation: The region bounded by an arc and a chord is called a segment.

Q3: What is the area of a sector of a circle with radius \( r \) and angle \( \theta \) degrees?

A: \( \frac{\theta}{180^\circ}\pi r^2 \)
B: \( \frac{\theta}{360^\circ}\pi r^2 \)
C: \( \frac{\theta}{90^\circ}\pi r^2 \)
D: \( \frac{\theta}{270^\circ}\pi r^2 \)

Explanation: The area of the sector is \( \frac{\theta}{360^\circ}\pi r^2 \).

Q4: What is the length of the arc of a sector of a circle with radius \( r \) and angle \( \theta \) degrees?

A: \( \frac{\theta}{180^\circ}\pi r \)
B: \( \frac{\theta}{360^\circ}\pi r \)
C: \( \frac{\theta}{360^\circ} 2\pi r \)
D: \( \frac{\theta}{180^\circ} 2\pi r \)

Explanation: The length of the arc is \( \frac{\theta}{360^\circ} \times 2\pi r \).

Q5: How is the area of a segment found?

A: Sector + Triangle
B: Sector − Triangle
C: Sector × Triangle
D: Sector ÷ Triangle

Explanation: Segment = Corresponding sector − Corresponding triangle.

Q6: What is the area of a 60° sector of a circle with radius 6 cm? (π = 22/7)

A: \( \frac{132}{7} \) sq cm
B: \( \frac{66}{7} \) sq cm
C: \( \frac{198}{7} \) sq cm
D: \( \frac{99}{7} \) sq cm

Explanation: \( \frac{60}{360} \times \frac{22}{7} \times 6^2 = \frac{132}{7} \).

Q7: What is the arc length of a 90° sector of a circle with radius 5 cm? (π = 22/7)

A: \( \frac{55}{7} \) cm
B: \( \frac{110}{7} \) cm
C: \( \frac{220}{7} \) cm
D: \( \frac{275}{7} \) cm

Explanation: \( \frac{90}{360} \times 2 \times \frac{22}{7} \times 5 = \frac{55}{7} \).

Q8: What is the area of a 60° segment of a circle with radius 10 cm?

A: \( 52.33 – 43.3 \)
B: \( 52.33 – 86.6 \)
C: \( 26.17 – 43.3 \)
D: \( 26.17 – 21.65 \)

Explanation: Segment = Sector − Triangle.

Q9: If the angle of a sector of a circle is 120°, what will be the angle of the remaining part?

A: 120°
B: 180°
C: 240°
D: 300°

Explanation: Remaining angle = 360° − 120° = 240°.

Q10: What is the sum of the angles of the minor and major sectors?

A: Same
B: 180°
C: 360°
D: Different

Explanation: Together they make the complete circle.

Q11: The area of a 30° sector is 15.7 sq cm. What will be the area of a 60° sector?

A: 7.85
B: 15.7
C: 31.4
D: 47.1

Explanation: Angle doubled, area doubled.

Q12: What is the area of a quadrant of a circle with radius 14 cm? (π = 22/7)

A: 154 sq cm
B: 77 sq cm
C: 308 sq cm
D: 38.5 sq cm

Explanation: \( \frac{1}{4} \pi r^2 \).

Q13: What is the sum of the areas of the minor and major segments equal to?

A: Half the circle
B: Area of the whole circle
C: Difference
D: Different

Explanation: Together they make the whole circle.

Q14: What is the area of a 60° sector of a circle with radius 21 cm? (π = 22/7)

A: 231 sq cm
B: 462 sq cm
C: 154 sq cm
D: 693 sq cm

Explanation: \( \frac{60}{360} \times \frac{22}{7} \times 21^2 = 231 \).

Q15: A wiper 25 cm long rotates through 115°. What will be the area cleaned?

A: \( \frac{115}{360} \times 3.14 \times 25^2 \)
B: \( \frac{115}{180} \times 3.14 \times 25^2 \)
C: \( \frac{115}{360} \times 3.14 \times 25 \)
D: \( \frac{115}{180} \times 3.14 \times 25 \)

Explanation: The area cleaned by the wiper is the area of a sector.

Quiz Results

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Class 10 Maths Chapter 11 Areas Related to Circles MCQs Quiz

Chapter 11, ‘Areas Related to Circles,’ is a very important and interesting chapter. In this chapter, you will review the formulas for the circumference and area of a circle and learn to apply them to more complex problems. You will learn to calculate the area of a sector and a segment of a circle. The chapter also includes questions on finding the area of figures formed by combining a circle with other shapes like a square or a triangle, which are frequently asked in the CBSE Class 10 Maths Quiz and board exams.

Conclusion

Scoring well in ‘Areas Related to Circles’ depends not just on memorizing formulas but on applying them correctly. Our Class 10 Maths Chapter 11 Areas Related to Circles MCQs Quiz is designed to help you master this skill. This quiz gives you practice on key topics like the Area of Sector and Segment and helps you make accurate calculations under exam pressure. By solving these objective questions, you can assess your preparation and gain the confidence to excel in your board exams. Start this Free Online Maths Quiz for Class 10 now!

FAQs on Class 10 Maths Chapter 11

1. Question: How many marks from the chapter Areas Related to Circles are asked in the board exam?
Answer: This chapter typically carries 6-7 marks in the CBSE board exam, including MCQs, short answer, and long answer questions.

2. Question: What are the most important formulas for this chapter?
Answer: The most important formulas are for the area of a circle (πr²), its circumference (2πr), the area of a sector, and the area of a segment.

3. Question: Is this Areas Related to Circles quiz based on the NCERT syllabus?
Answer: Yes, our Areas Related to Circles Class 10 quiz is fully based on the NCERT curriculum and the CBSE syllabus.

4. Question: How do you find the area of a sector of a circle?
Answer: If the central angle is θ, the area of the sector is (θ/360°) × πr², where ‘r’ is the radius of the circle.

5. Question: What is the difference between a sector and a segment of a circle?
Answer: A sector is the region between two radii and the connecting arc, while a segment is the region between a chord and the arc it subtends.

6. Question: Is this online quiz free?
Answer: Yes, this Free Online Maths Quiz for Class 10 is absolutely free. You can take it anytime and anywhere for practice.

7. Question: How should I prepare this chapter for the board exam?
Answer: First, memorize all the basic formulas. Then, solve the examples and exercise questions from the NCERT book. Finally, test your knowledge with our Areas Related to Circles Online Test.

8. Question: Does this quiz include questions on combinations of plane figures?
Answer: Yes, this quiz includes important questions on finding the area of combined figures like a circle within a square.

9. Question: What is the perimeter of a semi-circle?
Answer: If the radius is ‘r’, the perimeter of a semi-circle is πr + 2r (the sum of half the circumference and the diameter).

10. Question: What is the benefit of taking this online quiz?
Answer: This quiz helps you improve time management, check the accuracy of your formulas, and understand the exam pattern, which boosts your confidence and leads to better performance.

Test your knowledge with our free Class 10 Maths Chapter 11 Areas Related to Circles MCQs Quiz. Covers key topics like area of a sector, segment, and circumference. Perfect for CBSE board exam preparation. Practice now and excel!

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Areas Related to Circles MCQs Quiz

Quiz Results

Class 10 Maths Chapter 11 Areas Related to Circles MCQs Quiz

Conclusion

FAQs on Class 10 Maths Chapter 11

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